Your momentum is equal to the product of your mass and velocity. Earth’s gravitational acceleration is roughly 9.8m/s squared, so your momentum increases with time as you are pulled towards the core.

While you are falling down, the earth will start to continue to move in the direction it’s going, and since you are no longer being held down onto it, you will start slowly drifting towards the sides of the pit, where eventually you will make contact, unable to move yourself away from the sides. This will likely happen after you’ve reached significant downward velocity.

Anyway, we’re talking about a pit with no bottom, in a cartoon that’s making a joke.